A new result of the scaling law of weighted L1 minimization

TL;DR

This paper establishes a new sufficient condition for exact signal recovery using weighted L1 minimization in compressed sensing, revealing a direct relationship between weights and recoverability, supported by simulation results.

Contribution

It introduces a novel sufficient condition linking weights to recoverability in weighted L1 minimization, enhancing understanding of the scaling law in compressed sensing.

Findings

The sufficient condition accurately predicts the scaling law.

Simulation results validate the theoretical predictions.

The relationship between weights and recoverability is explicitly characterized.

Abstract

This paper study recovery conditions of weighted L1 minimization for signal reconstruction from compressed sensing measurements. A sufficient condition for exact recovery by using the general weighted L1 minimization is derived, which builds a direct relationship between the weights and the recoverability. Simulation results indicates that this sufficient condition provides a precise prediction of the scaling law for the weighted L1 minimization.